When measuring the voltage of a signal output from a lamp driver of a substrate process chamber, it is useful to compare the voltage of the signal output to the heat generated by lamps driven by the lamp driver. One common measurement used to analyze the voltage signal is the “peak voltage”, which is defined as the maximum magnitude of the voltage signal.
However, it is often more useful to represent a time-varying voltage signal by an average value that would correspond to an equivalent direct current (DC) voltage, where the corresponding DC current determines the energy loss or dissipated heat caused by applying a voltage across a resistor. A simple arithmetic average of the voltage over time is typically not useful because time varying signals, such as an alternating current (AC) signal in which the voltage varies sinusoidally between positive and negative values, often have an average voltage over time of approximately zero. A more useful value to represent the time varying voltage is the root mean square (“RMS”) value, which is the square root of the integral of the square of the voltage over time. The ratio of the peak voltage to the RMS voltage of a signal is known as the crest factor. Devices which determine RMS voltage of lamp drivers are known as RMS converters.
Error, in the context of RMS measurement, is defined by ignored energy of a measured signal due to the limiting dynamic range or spectrum of the measured signal. The inventors have observed that conventional RMS converters used in commercially available RMS voltmeters have low accuracy when used with signals having a high crest factor. For example, some conventional RMS meters have an approximate 4% error at a crest factor of 4. The error depends on the dynamic range and spectrum of a measured signal. However, the crest factor of pulse width modulated (PWM) signals, widely used in motor controllers and switching mode power supplies can be greater than 30. Therefore, measurements made by commonly used RMS meters give unacceptable results for PWM signals with a high crest factor.
Therefore, the inventors have provided methods and apparatus for providing more accurate RMS measurements of AC voltage signals generated by a lamp driver.